On the Approximability of Numerical Taxonomy (Fitting Distances by Tree Metrics)

  • Authors:

  • Richa Agarwala;Vineet Bafna;Martin Farach;Mike Paterson;Mikkel Thorup

  • Affiliations:

  • -;-;-;-;-

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 1999

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Abstract

We consider the problem of fitting an n × n distance matrix D by a tree metric T. Let $\varepsilon$ be the distance to the closest tree metric under the $L_{\infty}$ norm; that is, $\varepsilon=\min_T\{\parallel T-D\parallel{\infty}\}$. First we present an O(n2) algorithm for finding a tree metric T such that $\parallel T-D\parallel{\infty}\leq 3\varepsilon$. Second we show that it is ${\cal NP}$-hard to find a tree metric T such that $\parallel T-D\parallel{\infty}